High-angular resolution diffusion tensor imaging: physical foundation and geometric framework

This paper proposes a statistical physics-based data assimilation model for the mobility of water-bound hydrogen nuclear spins in the brain in the context of diffusion weighted magnetic resonance imaging (DWI or DW-MRI). Point of departure is a statistical hopping model that emulates molecular motion in the presence of static and stationary microscale obstacles, statistically reflected in the apparent inhomogeneous anisotropic DWI signal profiles. Subsequently, we propose a Riemann–Finsler geometric interpretation in terms of a metric transform that simulates this molecular process as free diffusion on a vacuous manifold with all diffusion obstacles absorbed in its geometry. The geometrization procedure supports the reconstruction of neural tracts (geodesic tractography) and their quantitative characterization (tractometry). The Riemann-DTI model for geodesic tractography based on diffusion tensor imaging (DTI) arises as a limiting case. The genuine Finslerian case is a geometric representation of high-angular resolution DTI , i.e., a generalized rank-two DTI framework without the quadratic restriction implied by a simplifying Gaussianity assumption on local diffusion or a second-order harmonic approximation of local orientation distributions.